Reservoir properties are sampled at well logs (wireline, LWD or cased-hole logs). Proper characterization of a reservoir, particularly for estimates of net rock volume, porosity volume, and original oil in place, requires an estimate of the property distributions of shale volume, porosity, saturation, etc. and the uncertainty of these property distributions. Property distribution uncertainty is a key component of reservoir characterization that affects volumetric uncertainty and reservoir recovery forecasts.
Typically a reservoir modeler will have no way to derive accurate distribution uncertainty for his model. Conventional statistical techniques of bootstrap are often used to assess the uncertainty of population statistics or property distribution (for example, as implemented in application Crystal Ball, developed by Oracle Corporation.
However, conventional bootstrap methods assume incorrectly that each property data collected is an independent measurement. Spatial bootstrap methods of Journel (A. G. Journel, “Resampling from stochastic simulations,” Environmental and Ecological Statistics, 1994, p. 63-91.) do not assume data independence. However, these methods are used solely to determine the uncertainty of the mean of the property distribution. These methods are not used to determine the uncertainty of the distribution itself.
Therefore, there is a need for a method of determining uncertainty of a property distribution such as, but not limited to, property distribution of shale volume, porosity, saturation, etc.